Effective and anomalous diffusion of inertial particles in flowing fluids

etc15 Tracking Number 331

We perform an analytical study of the inertial-particle dynamics in the limit of small but finite inertia, in incompressible flows, exploring their diffusion process. By means of a multiscale expansion, we analyse the particle effective diffusivity, and in particular its dependence on relative inertia, Brownian diffusivity, gravity, and particle-to-fluid density ratio (i.e. added mass). We obtain forced advection-diffusion equations for auxiliary quantities in the physical space, thus simplifying the problem from the full phase space to a system which can easily be solved numerically. In the case of parallel flows with power-law velocity spectra, we identify some cases of anomalous diffusion, according to the values of the exponents connected to the possible presence of long-range spatio-temporal correlations.